2 4*sin (t)
d / 2 \ --\4*sin (t)/ dt
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of sine is cosine:
The result of the chain rule is:
So, the result is:
Now simplify:
The answer is:
/ 2 2 \ 8*\cos (t) - sin (t)/